The girl, Autumn Carter, died because Smith was too drunk to realize his assault was killing her, Smith’s attorneys argued in court filings with the Ohio Parole Board, which heard the case Tuesday. And Ohio law is clear, they say: A death sentence requires an intent to kill the victim.

“The evidence suggests that Autumn’s death was a horrible accident,” Smith’s attorneys, Joseph Wilhelm and Tyson Fleming, said in a written argument prepared for the board.

They continued: “Despite the shocking nature of this crime, Steve’s death sentence should be commuted because genuine doubts exist whether he even committed a capital offense.”

Smith, 46, was never charged with rape, meaning the jury’s only choice was to convict or acquit him of aggravated murder, his attorneys say.

However, rape was included in the indictment against Smith as one of the factors making him eligible for the death penalty. Under Ohio law, an aggravated murder committed in the course of another crime — such as burglary, robbery, arson or the killing of a police officer or child — is an element that can make someone eligible for capital punishment.

The Richland County prosecutor said Smith continues to hide behind alcohol as an excuse and calls Smith’s actions “the purposeful murder of a helpless baby girl.”

Prosecutor James Mayer told the board in his written statement that the girl’s injuries were consistent with a homicide that contradicts Smith’s claim he didn’t intend to kill her.

Mayer said Monday he didn’t know why Smith wasn’t charged with rape, but he said it wasn’t part of a trial strategy.

The attack happened early in the morning of Sept. 29, 1998, in the Mansfield apartment of the girl’s mother, Kaysha Frye, whom Smith had been dating about six months.

Frye was awakened after 3 a.m. by a naked Smith, who placed Autumn beside her in bed, according to records prepared for the parole board hearing. Frye realized the girl wasn’t breathing, told Smith he’d killed her and then ran to a neighbor’s house for help.

Smith, known to consume as many as 12 beers a day, had had several beers the previous evening and had a blood-alcohol content of 0.123, well above the legal limit for drivers, when he was tested almost eight hours later, at 11 a.m., records show.

Smith had unsuccessfully tried to have sex with his girlfriend the evening before the attack, according to records. The prosecutor argued that Smith’s assault of the girl was revenge for Smith’s failure to perform with Frye.

Smith’s attorneys dispute this, saying the girlfriend was not upset with Smith.

Prosecutors presented evidence at trial that Smith’s attack lasted as long as 30 minutes, during which time Smith beat the girl to death.

Expert witnesses for Smith conclude he may have accidentally suffocated the girl within three to five minutes while he lay on top of her, according to Smith’s clemency petition.

Smith’s attorneys have an uphill battle in their argument because of the “moral repugnancy” surrounding the claim of partial innocence, said Doug Berman, an Ohio State University law professor and death penalty expert.

“But if the lawyers for this defendant can legitimately assert that the evidence doesn’t show or support that this was an intentional killing, not only is it appropriate to bring this up at clemency, I think they’re obliged, representing their client appropriately, to stress this point,” Berman said.

If executed, Smith would become the 51st inmate put to death in Ohio since the state resumed executions in 1999. The state has enough of its lethal injection drug, pentobarbital, to execute Smith and two other inmates before the supply expires. Eight more inmates are scheduled to die from November through mid-2015.

———Andrew Welsh-Huggins can be reached at https://twitter.com/awhcolumbus